I think using grids to build some hidey houses and places to climb is a great idea! It is secure as long as you get good quality grids that are all square, snap together, and use zip-ties to extra hold the grids together. There are a lot of options for how to floor those structures as well, and there are some examples in the RABBIT INFO section of this site, where you can see different habitats members have shared. For my grid-cages, I secure a sheet of cloroplast to the grid and lay cut carpet squares that you buy from hardware stores.

Different toy arrangements can be good for rabbits who engage with those toys, but if you feel your rabbit is board, I think making more structural environmental changes would be more enriching. At the same time, any animal would be naturally curious and want to explore more space where they suspect it is, so why should he be barred from going to the other place when everyone else can go (humorous interpretation of what’s going on in his mind, not me lecturing you!).

“… but he isn’t very interested in most toys unless they’re edible.” — This is an important observation. Trial and error is needed to figure out what individual rabbits like. If a rabbit isn’t interested in something, then that might be a personal taste and we need to find what they do like! This can include different sizes, materials, sounds, and “groundedness” (i.e. something that can be thrown around vs. attached and unmoveable). Some people talk about “toss” and “chew” toys, where chew toys are more anchored and take the place of rabbits who might like chewing baseboards in their free time.

I found binderclipping a bed sheet to the pen sides effective, but making sure it’s on the outside only, because if any drapes over the top to the inside or is too short and creates a fabric “step” up, my rabbits try to launch and climb up it:

I think structural changes are a good idea! My buns really like tunnels. I am currently in a similar situation, where I’m staying with my in-laws with 4 rabbits (AHH!), so the buns are in a room vs. having more of the house to roam in. To keep things interesting, I got some concrete building forms and made a cross shaped tunnel that they have been really enjoying running through and chewing on little bits of it (I imagine them working on their “burrow”).

Not sure what grows in your area, but palm fronds that have fallen down from palm trees are also really fun for bunnies to play under and chew on (so many textures and edges).

This is also kind of a counter-intuitive answer, but he might actually be more satisfied with his arrangement if you actually confined him to a pen for part of the day, and then let him out into the room for exercise another part of the day. I have just noticed with my buns, when they get 24/7 access to an area, they seem obsessed with the one spot they aren’t allowed to go (the grass is always greener I guess!). But when they get penned for a chunk of the day (mine currently get 12 hours in their condos, then 12 hours of roam time), they get excited about running around the new area when I let them out, and run around exploring and chinning everything. I think this could be especially effective if you rearrange his hides and toys when he is penned, then he gets a fresh place to play when he comes out.